Wells Fargo & Co. is expected to announce a restructuring of its wealth management business, according to people familiar with the matter, as it grapples with government investigations tied to client referrals and other related matters.

The bank is planning to combine two large divisions within the business, known internally as Wealth Brokerage Services and Private Client Group, the people said. Both are brokerages serving mass affluent customers. The private client group has about 9,500 brokers who work out of Wells Fargo’s...

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